A292843 Number of sets of nonempty words with a total of n letters over 9-ary alphabet.

1, 9, 117, 1542, 19404, 239481, 2900802, 34609797, 407615175, 4747112731, 54743025339, 625791326688, 7097863351275, 79938092898747, 894514969436076, 9951032414168964, 110103625982603466, 1212181195307220126, 13283829023674846878, 144946503880942833774

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{j>=1} (1+x^j)^(9^j).

a(n) ~ 9^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(9^(m-1)-1)) = 0.058648829660552563553047659756831342987... - Vaclav Kotesovec, Sep 28 2017

Maple

h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1)*binomial(9^i, j), j=0..n/i)))
    end:
a:= n-> h(n$2):
seq(a(n), n=0..30);

Crossrefs

Column k=9 of A292804.

Sequence in context: A139740 A221442 A196663 * A180904 A062994 A059967

Adjacent sequences: A292840 A292841 A292842 * A292844 A292845 A292846

Keyword

nonn

Author

Alois P. Heinz, Sep 24 2017

Status

approved